作物害虫化学防治的数学模型  

Mathematical model of chemical control of crop pest

作　　者：程述汉[1] 徐臣善[2] 李明[3] 辛泽山 束怀瑞[2] 王衍安[4] 

机构地区：[1]山东农业大学信息科学与工程学院,泰安271018 [2]山东农业大学园艺科学与工程学院,泰安271018 [3]国家农业信息化工程技术研究中心,北京100097 [4]山东农业大学生命科学学院,作物生物学国家重点实验室,泰安271018

出　　处：《农业工程学报》2008年第S2期32-35,共4页Transactions of the Chinese Society of Agricultural Engineering

基　　金：国家863计划(2008AA10Z219);山东省自然科学基金(Y2002D14)

摘　　要：为了实现植物化学保护的精确化与数量化,该文研究化学药物控制害虫的数学模型,在充分考虑喷施农药后药效持续发挥作用阶段害虫密度的变化动态,以及药物失效后与首次喷施农药前内禀增长率的差异的基础上,建立了施药前后3个阶段的微分方程模型,给出了模型的周期解,从而确定了喷施农药周期,为合理用药、保障食品安全提供理论依据。文中所建模型由3个Logistic模型构成,具有易求解和易使用的特点;对实际观测数据的拟合结果表明,该模型具有可靠性和实用性。In order to achieve accuracy and quantification of chemical protection of plants,the mathematical model of chemical pest control was studied.With a thorough consideration of both the dynamic state of the pest population density in the period after fog spraying during which the insecticide still effects and the difference of the intrinsic increasing rate between before first spray insecticide and after the pesticide invalidation,the differential equation models for the three different stages before,in and after the spray were established,and the periodic solutions of the models were given,thus the cycle of periodic spray was established for supplying a theoretical evidence for rational and reasonable using of insecticide and for ensuring food safety.The model established in the paper consists of three Logistic Models characterized by solution-prone and manipulation-prone.It is indicated by the model fitting results for using observed data that the model is of reliability and practicability.

关 键 词：害虫 农药 数学模型 周期解 

分 类 号：S433[农业科学—农业昆虫与害虫防治]